Showing papers on "Quantum evolution published in 1999"
TL;DR: In this article, the authors consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory and find that the reduced density matrix can display dynamics given by L\'evy stable laws.
Abstract: Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by L\'evy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular, we derive a fractional extension of Kramers equation.
266 citations
TL;DR: In this article, a quantum evolution model in 2 + 1 discrete spacetime, connected with a 3D fundamental map, is investigated, and a generating function for the integrals of motion for the evolution is derived with the help of the current system.
Abstract: A quantum evolution model in 2 + 1 discrete spacetime, connected with a 3D fundamental map , is investigated. Map is derived as a map providing a zero curvature of a 2D linear lattice system called `the current system'. In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical and it corresponds to the known operator-valued -matrix. The current system is a type of the linear problem for the 2 + 1 evolution model. A generating function for the integrals of motion for the evolution is derived with the help of the current system. Thus, the complete integrability in 3D is proved directly.
49 citations
TL;DR: In this paper, the authors characterize good clocks in statistical terms and obtain the master equation that governs the evolution of quantum systems according to these clacks and find its general solution, which is diffusive and produces loss of coherence.
Abstract: We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clacks and find its general solution. This master equation is diffusive and produces loss of coherence, Moreover, real clocks can he described in terms of effective interactions that are nonlocal in time. Alternatively, they can be modeled by an effective thermal bath coupled to the system. [S1050-2947(99)04905-7].
31 citations
TL;DR: In this article, the authors consider the revival properties of quantum systems with an eigenspectrum En n2, and compare them with the simplest member of this class -the infinite square well.
Abstract: We consider the revival properties of quantum systems with an eigenspectrum En n2, and compare them with the simplest member of this class - the infinite square well. In addition to having perfect revivals at integer multiples of the revival time tR, these systems all enjoy perfect fractional revivals at quarterly intervals of tR. A closer examination of the quantum evolution is performed for the Poschel-Teller and Rosen-Morse potentials, and comparison is made with the infinite square well using quantum carpets.
24 citations
TL;DR: In this article, the authors generalized the Lewis-Riesenfeld invariant theorem to open systems of quantum fields after second quantization, and the generalized invariants and quantum evolution were found explicitly for time-dependent quadratic fermionic systems.
Abstract: Open systems acquire time-dependent coupling constants through interaction with an external field or environment. We generalize the Lewis-Riesenfeld invariant theorem to open system of quantum fields after second quantization. The generalized invariants and thereby the quantum evolution are found explicitly for time-dependent quadratic fermionic systems. The pair production of fermions is computed and other physical implications are discussed.
13 citations
01 Jan 1999
TL;DR: It was revealed that the QCMD model is of canonical Hamiltonian form with symplectic structure, which implies the conservation of energy, and an efficient and reliable integrator for transfering these properties to the discrete solution is the symplectic and explicit PICKABACK algorithm.
Abstract: It was revealed that the QCMD model is of canonical Hamiltonian form with symplectic structure, which implies the conservation of energy. An efficient and reliable integrator for transfering these properties to the discrete solution is the symplectic and explicit PICKABACK algorithm. The only drawback of this kind of integrator is the small stepsize in time induced by the splitting techniques used to discretize the quantum evolution operator. Recent investigations concerning Krylov iteration techniques result in alternative approaches which overcome this difficulty for a wide range of problems. By using iterative methods in the evaluation of the quantum time propagator, these techniques allow for the stepsize to adapt to the classical motion and the coupling between the classical and the quantum mechanical subsystem. This yields a drastic reduction of the numerical effort. The pros and cons of both approaches as well as the suitable applications are discussed in the last part.
13 citations
TL;DR: In this paper, a quantum Markov partition is constructed by quantizing the characteristic function of the classical rectangles, and a set of quantum operators are shown to behave asymptotically as projectors over these rectangles.
Abstract: We present a method for constructing a quantum Markov partition. Its elements are obtained by quantizing the characteristic function of the classical rectangles. The result is a set of quantum operators which behave asymptotically as projectors over the classical rectangles apart from edge and corner effects. We investigate their spectral properties and different methods of construction. The quantum partition is shown to induce a symbolic decomposition of the quantum evolution operator. In particular, an exact expression for the traces of the propagator is obtained having the same structure as the Gutzwiller periodic orbit sum.
12 citations
TL;DR: In this article, a quantum Markov partition is constructed by quantizing the characteristic function of the classical rectangles, and a set of quantum operators are shown to behave asymptotically as projectors over these rectangles except from edge and corner effects.
Abstract: We present a method for constructing a quantum Markov partition. Its elements are obtained by quantizing the characteristic function of the classical rectangles. The result is a set of quantum operators which behave asymptotically as projectors over the classical rectangles except from edge and corner effects. We investigate their spectral properties and different methods of construction. The quantum partition is shown to induce a symbolic decomposition of the quantum evolution operator. In particular, an exact expression for the traces of the propagator is obtained having the same structure as Gutzwiller periodic orbit sum.
10 citations
01 Jan 1999
TL;DR: In this article, the quantum trajectory theory of photon scattering in quantum optics is reviewed and two features of the theory which bear closely on issues of interpretation in quantum mechanics are emphasized: (1) there exist different unravellings of a scattering process which reveal complementary aspects of the dynamics in the interaction region, and (2) through the making of records via a stochastic implementation of a formalized quantum jump a selfconsistent interface between a quantum evolution (in Hilbert space) and a classical evolution for the records (time series of real numbers) is achieved.
Abstract: The quantum trajectory theory of photon scattering in quantum optics is reviewed Two features of the theory which bear closely on issues of interpretation in quantum mechanics are emphasized: (1) there exist different unravellings of a scattering process which reveal complementary aspects of the dynamics in the interaction region, and (2) through the making of records via a stochastic implementation of a formalized quantum jump a self-consistent interface between a quantum evolution (in Hilbert space) and a classical evolution for the records (time series of real numbers) is achieved
8 citations
01 Jan 1999
TL;DR: Those typical problematic situations where a mixed model might largely deviate from the full quantum evolution are characterized, and a nonadiabatic excitation at certain energy level crossings can promisingly be dealt with by a modification of the QCMD model.
Abstract: In molecular dynamics applications there is a growing interest in including quantum effects for simulations of larger molecules. This paper is concerned with mixed quantum-classical models which are currently discussed: the so-called QCMD model with variants and the time-dependent Born-Oppenheimer approximation. All these models are known to approximate the full quantum dynamical evolution—under different assumptions, however. We review the meaning of these assumptions and the scope of the approximation. In particular, we characterize those typical problematic situations where a mixed model might largely deviate from the full quantum evolution. One such situation of specific interest, a nonadiabatic excitation at certain energy level crossings, can promisingly be dealt with by a modification of the QCMD model that we suggest.
8 citations
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TL;DR: A procedure for adjustment of the singlet evolution of a quantum computation to a classical signal input by action potentials will be described and a model for the generation of quantum coherence in a single neuron will be suggested.
Abstract: Current quantum theories of consciousness suggest a configuration space of an entangled ensemble state as global work space for conscious experience. This study will describe a procedure for adjustment of the singlet evolution of a quantum computation to a classical signal input by action potentials. The computational output of an entangled state in a single neuron will be selected in a network environment by "survival of the fittest" coupling with other neurons. Darwinian evolution of this coupling will result in a binding of action potentials to a convoluted orbit of phase-locked oscillations with harmonic, m-adic, or fractal periodicity. Progressive integration of signal inputs will evolve a present memory space independent from the history of construction. Implications for mental processes, e.g., associative memory, creativity, and consciousness will be discussed. A model for the generation of quantum coherence in a single neuron will be suggested.
TL;DR: In this article, it was shown that the time dependent equations for a quantum system can be derived from the time independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically.
Abstract: It is shown that the time-dependent equations (Schrodinger and Dirac) for a quantum system can be always derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion-atom collisions, where it appears as a transition from the full quantum mechanical {\it perturbed stationary states} to the {impact parameter} method in which the projectile ion beam is treated classically.
TL;DR: In this paper, the Schroedinger operator on graphs is studied and the spectral statistics of a unitary operator which represents the quantum evolution of a quantum map on the graph are derived.
Abstract: We consider the Schroedinger operator on graphs and study the spectral statistics of a unitary operator which represents the quantum evolution, or a quantum map on the graph. This operator is the quantum analogue of the classical evolution operator of the corresponding classical dynamics on the same graph. We derive a trace formula, which expresses the spectral density of the quantum operator in terms of periodic orbits on the graph, and show that one can reduce the computation of the two-point spectral correlation function to a well defined combinatorial problem. We illustrate this approach by considering an ensemble of simple graphs. We prove by a direct computation that the two-point correlation function coincides with the CUE expression for 2x2 matrices. We derive the same result using the periodic orbit approach in its combinatorial guise. This involves the use of advanced combinatorial techniques which we explain.
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TL;DR: In this article, the authors apply the Liouville-von Neumann (LvN) approach to open systems to describe the nonequilibrium quantum evolution of oscillator models for open boson and fermion systems.
Abstract: We apply the Liouville-von Neumann (LvN) approach to open systems to describe the nonequilibrium quantum evolution. The Liouville-von Neumann approach is a unified method that can be applied to both time-independent (closed) and time-dependent (open) systems and to both equilibrium and nonequilibrium systems. We study the nonequilibrium quantum evolution of oscillator models for open boson and fermion systems
Journal Article•
TL;DR: In this paper, the authors introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks and show that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties finding application in pattern recognition, optimization and simulation.
Abstract: We introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks. We show that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties finding application in pattern recognition, optimization and simulation. Moreover, decoherence in quantum recurrent networks is less problematic than in conventional quantum network architectures due to the modest phase coherence times needed for network operation.